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Paper Citation Record · LEDGER

Stability and Synchronization of Kuramoto Oscillators

As of 13 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2411.17925.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2411.17925 v2

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T11:53:24.565038Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a9c6794d-15a0-4e51-8167-8ed799efa4b8 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.254757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.601352Z digest=sha256:a87cf0d47f17450bd28aee7b2501383910f0cac5f5fa2562942f1181f5f7e1e6

Observation 2fe3ebdf-c16b-417c-ac92-afa92559943d · outbound

This paper cites In essence, sufficiently strong coupling ensures the existence (and, at an even higher threshold, unique- ness) of a stable phase-locked solution.

Stability and Synchronization of Kuramoto Oscillators In essence, sufficiently strong coupling ensures the existence (and, at an even higher threshold, unique- ness) of a stable phase-locked solution

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.241714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.647517Z digest=sha256:5dd06399660828089c07fa1fe65d3ffd330a38f5877dc2012c1e92a4c7bd5855

Observation c51cbefe-67ba-4e78-a2ed-33e99475faa4 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.225959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.710593Z digest=sha256:9dce9d9caac8846ffa2fa36947db4ae8f76095838edb36a52d5d11422bb51a81

Observation 1c31ad93-29c8-40a6-8c65-0dd3bd3fcbf3 · outbound

This paper cites Before moving to the next notion of synchronization, let us look at a few mathematical preliminaries.

Stability and Synchronization of Kuramoto Oscillators Before moving to the next notion of synchronization, let us look at a few mathematical preliminaries

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.185427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.774262Z digest=sha256:0755a75c33bba8e083065294f9a07fc6da27553027e64df8abfbad4e58bfddcb

Observation 94bd220e-4089-4c1e-a691-a1718a31dee2 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.075786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.806895Z digest=sha256:c59751e38693d15d03cb3e2e050cff906047843f0c735fe2a3d3e535cb2d5981

Observation 748675df-7e30-48d3-b5b6-b104359a0a50 · outbound

This paper cites For example, a solution θ : R≥0 → Tn achieves phase synchronization if limι→∞ |θi(t) − θj(t)| = 0.

Stability and Synchronization of Kuramoto Oscillators For example, a solution θ : R≥0 → Tn achieves phase synchronization if limι→∞ |θi(t) − θj(t)| = 0

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.029428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.837979Z digest=sha256:4c1a256f88b58d6b8f11d5eff32f7f8213f3f50f00ec9512abc0ae6aed523064

Observation 59b7265d-d51b-41a1-b2df-f5be71c366c1 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.015879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.851501Z digest=sha256:e8a885718ce1d32a90c509b77197dcf85e77ee25b83be5f7b8f243d14326dc57

Observation a41f9fd7-a2ca-4ee4-bcea-9e106be84331 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.999644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.857035Z digest=sha256:36943e066712007c9841a0d8d7d0d20b3d6200e7a8d8f57c4a58c2945f0121fd

Observation 776a7684-11f8-4938-b94b-b37785bda508 · outbound

This paper cites Proof: Given θ ∈ Tn, we define the undirected graph Gcosine (θ) with the same nodes and edges as G and with edge weights aij cos (θi − θj).

Stability and Synchronization of Kuramoto Oscillators Proof: Given θ ∈ Tn, we define the undirected graph Gcosine (θ) with the same nodes and edges as G and with edge weights aij cos (θi − θj)

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.911693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.898311Z digest=sha256:ba074a950866fdb2edeefea3381ad34b95f72e2dc5bada3c1aaa1b29d0e476d2

Observation 14a1bdd9-9618-4a56-9d07-f7ea89ca8101 · outbound

This paper cites Strogatz, ”From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators”, Physica D: Nonlinear Phenomena, Volume 143, Issues 1–4, 2000.

Stability and Synchronization of Kuramoto Oscillators Strogatz, ”From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators”, Physica D: Nonlinear Phenomena, Volume 143, Issues 1–4, 2000

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.804586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:23.963578Z digest=sha256:987f127fd6925cfde51d5b61a048d3a6c5953c7102b6fd2fd4eab5182d59ebb5

Observation 63f2757b-a2ae-4a09-a6dc-c73cf4c34281 · outbound

This paper cites Godsil and G.

Stability and Synchronization of Kuramoto Oscillators Godsil and G

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-12T11:53:24.023948Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T11:53:24.023948Z digest=sha256:dafade58251c10938aaca4efde52e0156659055d1bcbf43065b5f5208d1058f2

Observation ccfbdefa-f528-42f7-87fa-b499804eeed9 · outbound

This paper cites Biggs, Algebraic Graph Theory, Cambridge University Press, 1993.

Stability and Synchronization of Kuramoto Oscillators Biggs, Algebraic Graph Theory, Cambridge University Press, 1993

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.777977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.089395Z digest=sha256:ff7e4bf0096e0fcfeb649c076c27c0f4d965aa591752fc7de6625653cf3fcb54

Observation 71702fcc-fba8-414c-9bdd-0ec42eb905c0 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.728850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.125902Z digest=sha256:3e6fffd8cf240ee9e931c727d76bd2c4730c64eaf789c9fa8afa39c9cce8e8d4

Observation 50f3300c-80b3-43da-bdc6-4f14c8b4f5cf · outbound

This paper cites Chopra and M.

Stability and Synchronization of Kuramoto Oscillators Chopra and M

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-12T11:53:24.191645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T11:53:24.191645Z digest=sha256:bb42c5c8d996d6707c81c64df0d31d70b3e290454dc9454ec26eddfec8c38770

Observation 7d8da27b-ffae-4310-b671-5e1fcab123df · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.609506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.230088Z digest=sha256:80cc4c427aacfe0dacf2ed7c09547c2046cf3cd3544e3c352cd73881f4b845a0

Observation a3046708-4302-4b34-8429-d6877d3e427a · outbound

This paper cites D¨ orfler, M.

Stability and Synchronization of Kuramoto Oscillators D¨ orfler, M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.489704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.252517Z digest=sha256:18317697ee8b5573545baab9ab818c96fd0384a129818a74a2e91196bef89024

Observation 7226edea-8714-4b7f-9b34-d3b96b50d751 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.476039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.279042Z digest=sha256:b26413e45338c5f46b6073dff4bf5fc525c15453536d4e077d4eb76dc561d18a

Observation 8a619fa8-b299-42b0-aad6-73fbc209711c · outbound

This paper cites Chepizhko, V.L.

Stability and Synchronization of Kuramoto Oscillators Chepizhko, V.L

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.456720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.288168Z digest=sha256:7ac84d96c18b932c3ac4886fe0da3ad29ec0d37c32844e83fda33f44ac581971

Observation ea115649-4389-466a-ad60-b0be28fc86cc · outbound

This paper cites The Kuramoto Model.

Stability and Synchronization of Kuramoto Oscillators The Kuramoto Model

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.408079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.292457Z digest=sha256:cd6d375f551b8dae629e41d1760004cfa0abf1af98238211f85c4f02dcb966a7

Observation af9591bd-5733-4456-9c29-9e29aa6aeae1 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.361758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.296805Z digest=sha256:1c9f1a86de59316f4b9b93f07c1510fe99f4bc21cccdf98f6751c06bf51862e5

Observation c7567a3f-13ec-431e-836c-16a37d33d83b · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.238470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.301287Z digest=sha256:c82bb2f248a247f5e2f4b7e1bc47dd55066f841f1cb8b1b9ec45bac759c28afd

Observation 42242f9b-1465-424f-9aa7-0522719904e4 · outbound

This paper cites Strogatz.

Stability and Synchronization of Kuramoto Oscillators Strogatz

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.105216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.310169Z digest=sha256:93abd25e49ef148ec514da1e3563c66f41dbb30235602ddfdf5b80f347003070

Observation f46012c9-3e0f-4603-b84d-973845188395 · outbound

This paper cites Synchronization: From Simple to Complex.

Stability and Synchronization of Kuramoto Oscillators Synchronization: From Simple to Complex

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.052640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.403393Z digest=sha256:ddaf6cc97410c4c617ecd2497f4bf82406a5a4e938a026ad42945dfca7940eb5

Observation 556e907d-1f8d-450e-8624-96bb59cba5d3 · outbound

This paper cites Acebr, L.L.

Stability and Synchronization of Kuramoto Oscillators Acebr, L.L

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:24.896053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.478508Z digest=sha256:c01781f669d5ff5c47414ce4a66b8cad85880ffe99e8ac8decfbf19f43b1aeef

Observation 0b855058-08ce-415a-a567-cc339680b89f · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:24.831705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.525943Z digest=sha256:4dd4647ccbb841f4cff082c5a1582f22bc1f4fadf36c104847c748673ac8cd67

Observation 7f5c1611-904d-4f39-a9f3-c98afec4b301 · outbound

This paper cites optimal,” (1994) 21.

Stability and Synchronization of Kuramoto Oscillators optimal,” (1994) 21

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:24.730006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-12T11:53:24.565038Z digest=sha256:4018a1e7314ca5466f10744fe29a9337bca185d0c32f3350b1d63f38d22c22a4

Pith citing papers

No inbound Pith citation observations are available.